Can recurrent-in-space and recurrent-in-time circuits learn complex patterns similar to those generated by traditional NCAs?

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• Euclidean rhythms demonstrate how simple patterns generate complex organized structures.claim0.741
• Emergence of grid-like representations by training recurrent neural networks to perform spatial localization (Cueva & Wei, 2018)concept0.739
  RNN model recapitulating grid cells; related work category 4.
• NCA do not inherently operate within a discrete state space, making interpretability more challenging and requiring costly matrix multiplications on current hardwareclaim0.737
  Authors' critique of NCA motivating the DiffLogic CA approach
• Deep representations have a special significance in recurrent networks, allowing coordinated behaviour without losing sensitivity to new inputs.claim0.732
  Importance of hierarchical structure for flexible coordination.
• Alternating repetition appears in nature where secondary repeating centers are coherent, e.g., waves and troughs, stripes and spaces.claim0.730
• Multiscale systems like those prevalent in biology are capable of organizing into complex patterns, whereas rudimentary language models are challenged by long sequences of outputs.claim0.726
  Conclusion about why biology organizes complexity well and flat LLMs do not
• Algorithmic recurrence is likely necessary for conscious experience with human-like temporal character.claim0.725
  Support for RPT-1.
• Reinforcement learning acting on individual characteristics affecting their connections to others can result in dynamics that are equivalent to unsupervised learning at the system scale.claim0.724
  Key insight linking individual rewards to system-level learning.